An efficient solution procedure is developed for a nonseparable semigeostro
phic Eady problem an a semiinfinite f plane. A model is designed to study t
he effects of meridionally isolated jets and tropopause morphology on baroc
linic instability. Potential vorticity (PV) is assumed to be piecewise cons
tant and discontinuous at the tropopause, whose height is allowed to vary w
ith latitude. The computational domain is discretized in a stretched coordi
nate to maintain adequate resolution in the vicinity of the tropopause and
axis of the jet. The basic state is numerically inverted from the two PV va
lues with the specification of only the meridional profiles of potential te
mperature (PT) at the surface and (unspecified) tropopause height. The nons
eparable eigenvalue problem about this basic state is solved for the discre
te (zero-PV) normal modes. Since continuum modes are not sought, the size o
f the problem is reduced greatly, keeping the storage and CPU requirements
moderate even at relatively high spatial resolutions.
This model is used to investigate changes in the zonal-mean state and the s
tability thereof, in response to arrangements of the zonal-mean PT at the s
urface and tropopause. In particular, (a) partial mixing of surface PT and
(b) appearance of a local minimum of PT on the tropopause are considered as
models of baroclinic adjustment and tropopause folds, respectively. The fo
rmer renders the mean flow more barotropic and shifts up the zonal scale of
baroclinic instability. The latter gives rise to a markedly dipped tropopa
use that is barotropically unstable at various ranges of wavenumbers. The r
esults' implications on the life cycle simulations and roll-up of stratosph
eric intrusions are discussed.